Bloom effect with a transparent background?
I have tested many different combinations.
The best way to achieve it is to use post compositing.

With cycle follow the node setup with red arrows.
I also tried EEVEE, there is a BloomCol pass that you can check,
but this pass does not have tranparency, so using this or doing an alphaover node would kill your transparency. It does look fancier out of box.

but for transparency I think cycles is easier.
I am sorry if it looks messy, as I just figured it out, so I do not want to destroy my node setup.